Just over a week ago, a group of campaigners gathered outside the News International offices in east London with a birthday card for the Sun.

The occasion? The 42nd anniversary of Page 3. The card was 6ft high, and while one side showed how women are portrayed in some of the tabloids – topless images from the Sun and the Star, as well as semi-naked, bent-double images from the Sport — the other showed how men are portrayed. The crucial difference could be summarised in the single word "clothes"; more broadly, men were pictured as active, respected professionals. The protesters wrote their feelings about Page 3 in the card. "A woman is worth more than her cup size," scrawled one. "Still stuck in the sexist, Savile-loving 70s, Dominic?" asked another.

The Facebook and Leveson censorship should be surprising because, as Van Heeswijk says, "these are images that are contained within our national newspapers, completely available to all, mainstream, unrestricted, sold in newsagents and supermarkets."

The Page 3 protest is just one of an extraordinary number of current campaigns against media sexism. Over the past few years, and particularly the past few months, anger about the media portrayal of women, in terms of visibility, sexualisation and humiliation, has grown at feverish pace. Along with the campaigns to end Page 3 are projects to highlight the paucity of female experts in broadcasting and the dearth of older women on TV, to make it easier for journalists to find female speakers, to show how media sexism affects women on a personal level, and clarify just how it feeds into a culture in which women's confidence is undermined, ambitions narrowed, and experiences of rape and violence disbelieved. There's a growing sense this could be a watershed moment, when coverage genuinely changes for the better.

The four groups behind the report Just the Women certainly hope so. (Their title is, of course, a reference to the now-notorious comment from Newsnight editor Peter Rippon that the show's Jimmy Savile investigation needed more work, since the sources were "just the women".) Eaves, End Violence Against Women (Evaw), Equality Now and Object all presented evidence to Lord Justice Leveson this year, and he reports back on Thursday. To sharpen and renew the focus on these issues they have carried out an evaluation of the press, charting examples of sexism.

What was most surprising, says Julia Hilliard, a feminist activist and volunteer at Eaves, was the sheer volume of sexist content. In 11 national newspapers, over two weeks, they found more than 1,300 examples. "It's easy to laugh off or dismiss individual examples as, 'You're reading too much into it, it's a joke'," she says. "But cumulatively, it's a barrage." Analysing the material "felt like being insulted constantly, just being belittled and degraded and put in your place".

Another researcher, Roxanne Halsey, says the experience demonstrated very clearly to her how sexist media affects women. The mocking coverage of female politicians, for instance, knocked her confidence, and left her feeling that: "This is what happens to women who are prepared to be in the public eye – you get insulted by both men and women." She volunteers at Eaves twice a week, and wouldn't have wanted to work on the project more than that. "Of course, you can imagine what it's like looking at photos of women's breasts for days … but that doesn't change the fact that you look at these photos, and you start thinking about your own body." Being able to analyse the material from a feminist perspective didn't neutralise its effects, she says.

'These are images that are contained within our national newspapers, completely available to all' … anti-Page 3 campaigner Anna van Heeswijk. Photograph: Katherine Rose Katherine Rose for the Observer

The report pinpoints a number of problem areas. One is the tendency to sexualise young girls, while purporting to condemn this; in the two-week period, a child beauty pageant was covered enthusiastically by many of the tabloids, which ran numerous photographs alongside critical articles. For instance, the Sun ran a piece with pictures and the subheading "CAVORTING provocatively in a tiny pink swimsuit and clutching a cuddly stuffed kitten, little Ocean Orrey struts her stuff in a British beauty pageant – aged just FOUR."

When reporting crimes against women, there was a tendency to trivialise the event, and to empathise with the perpetrator, "by eulogising their achievements, and highlighting their careers, their celebrity, and their supposed respectability". In coverage of female politicians, there was a tendency to mock them. And, of course, there are all those images highlighted by the Page 3 protest.

The report mentions the 16 September cover of the Sunday Sport, for example, in which a picture of a woman's bottom ran beside the headline "Katy Perry Upskirt Photo Shock". This isn't especially unusual for the Sport. Its midweek edition launched last year with a front page close-up of a woman's crotch, above the headline "Cheryl Cole Upskirt Pic Shock" and last week TV presenter Holly Willoughby complained to the Press Complaints Commission over a fake upskirt photo of her in the Sunday edition. Her complaint was addressed with a front-page apology this week, which admitted: "Contrary to the clear impression that we give in the edition, no part of the 'upskirt' photograph was of Holly Willoughby." This apology ran above images of a young Coronation Street actor in a bikini – the main cover picture showing her bent over, from behind.

It's often unclear whether upskirt shots are staged or real, consensual or not. But whatever the circumstances, these shots "make the link between the sexualisation in the papers and violence against women really clear," says Holly Dustin, director of Evaw, because "the implication, either way, is that it's non-consensual, and that it's sexual exploitation being presented for our entertainment."

Arguments have long been made against the idea that media sexism genuinely affects how we view and treat women, but over the past year, various sources have disputed this. In January, for instance, Alison Saunders, head of the Crown Prosecution Service in London, suggested the media portrayal of young women could affect juries in rape trials. "If a girl goes out and gets drunk and falls over," she said, "they are almost demonised in the media, and if they then become a victim, you can see how juries would bring their preconceptions to bear."

Not long afterwards, a survey of 1,600 women, conducted by website Mumsnet, found one in 10 had been raped, four-fifths of those who had been assaulted hadn't reported it, and 70% felt the media were unsympathetic to women who report rape – considerably more than the 53% who felt the legal system lacked sympathy. Then there's the Savile scandal. Since the stories of his crimes began being reported, rape helplines have seen an enormous rise in calls, which shows what happens when victims of sexual violence are believed and taken seriously. This raises the obvious question: what happens when, as is more usually the case, they're not?

A new website, Everyday Media Sexism, also allows women to recount their first-person experiences – it follows and builds on the success of the website Everyday Sexism started by writer and women's activist Laura Bates earlier this year. The site includes a submission from a woman who recalls sitting on a bus, aged 14, in her school uniform, alongside a middle-aged man who was looking at Page 3. He turned to her chest, and remarked: "I wouldn't worry – with tits like yours, they're not going to ask you to pose."

It's sobering to think that the most prominent image of a woman in our papers each day is of a teenager or twentysomething in her pants; the Sun does, after all, have the highest circulation of any British newspaper, and Page 3 is its most famous feature.

It would help if there were at least more positive images of women, and more women's voices, to balance this out. But as numerous projects have shown, this is far from the case. A Women in Journalism report last month, for instance, which I was involved in, found women write only 22% of front-page articles, and account for just 16% of those mentioned or quoted in lead stories. An analysis of the first person mentioned in each front-page lead story found three-quarters of the expert voices were men, and 79% of victim's voices were women. When it came to the 10 people pictured most frequently on our front pages in the specific month we looked at, three were female – the Duchess of Cambridge, a woman defined by her marriage; Pippa Middleton, a woman defined by her sister's marriage; and Madeleine McCann, the young victim of an abduction. By comparison, the men pictured most frequently on the front pages were known primarily for professional reasons.

Lis Howell, director of broadcasting at City University, has been working on the Expert Women campaign, in conjunction with Broadcast magazine, since last February; she and her students have been monitoring the proportion of women used as experts on various TV and radio programmes since 2009. BBC News at Ten recorded its worst ever score on Thursday 25 October, when it featured 13 male experts and one female expert. As part of the campaign, the magazine has created a pledge for broadcasters, asking them to aim for 30% of on-air experts to be women; Sky News and Channel 4 have signed up, but the BBC refused.

What's interesting, says Howell, is that while people often argue that "women get a raw deal in television because appearance is so important, in that case why aren't there more women on radio? Radio is actually overall worse and more sexist." The Today programme is particularly bad, she says, which became clear earlier this month when, on consecutive days, it featured a conversation among male experts about teenage contraception, then three men talking about breast cancer.

Page 3 protesters compare the tabloid representation of men and women: 'The crucial difference could be summarised in the single word "clothes".' Photograph: Leon Neal/AFP/Getty Images

Those incidents inspired feminist writer Caroline Criado-Perez and Catherine Smith to set up the website thewomensroom.org.uk, a database of female experts. In just three weeks, more than 1,000 women have signed up, which contradicts the notion that women aren't interested in public speaking. Similarly, a recent training course for potential female broadcasters, organised by the BBC, had more than 500 applicants for 33 places.

Of course, media sexism often intersects with other forms of discrimination. The Just the Women report points out that tabloid images of women are "overwhelmingly white, young, able-bodied and thin", then notes, depressingly, that one place where "images of older and black and minority ethnic (BME) women were found was within the pages of adverts for the sex industry contained within some of these publications".

Last year Chitra Nagarajan, a member of the activist group Black Feminists, started the influential "diversity audit" hashtag on Twitter, for people to log male or female representation, as well as the representation of other groups. And Miriam O'Reilly – who was dropped from the TV show Countryfile in 2009, and went on to win an ageism claim against the BBC – has been working tirelessly to improve the media representation of older women. She is currently working on a Labour commission on the portrayal of older women in the media and public life, and feels the issue is "really in the public consciousness now. I've had older women run after me in the street and put their arms around me, and say they feel we're overlooked."

She's hoping the commission will prompt genuine change, and says Labour hasn't ruled out legislation on the issue. Criado-Perez hopes to make The Women's Room a site where women can network too, and Howell says the Expert Women campaign will continue until "the day the Today programme has reached, consistently, at least three to one women experts." Given that only around 18.5% of its reporters and guests are currently women, it could be some time.

The groups behind Just the Women have spelled out the changes they are hoping to see too. For instance, under any new press regulatory body, they would like it to be possible to make third-party complaints, as well as thematic complaints – so if an issue such as rape or domestic violence is regularly covered in a problematic way, that could be addressed. They also argue that sexually explicit images, which aren't allowed on TV before the 9pm watershed, and aren't allowed in the workplace under equality legislation, should not be printed "in national newspapers which are not age-restricted and are displayed at child's eye level".

On Thursday they will see if those and other suggestions are successful.

But whatever Leveson decides, it seems unlikely women will stop protesting about media sexism, much of which looks especially anachronistic in the wake of the Savile revelations. As Van Heeswijk points out: "Page 3 was launched in 1970, when there was no equality legislation, sexual harassment wasn't recognised in law, and rape in marriage was legal. It's now 2012. Isn't it time we got rid of this form of sexism from our press?"